Minimum number of operations required to sum to binary string S using C++.

Problem statement

Given a binary string str. Find the minimum number of operations required to be performed to create the number represented by str. Only following operations can be performed −

• Add 2^x
• Subtract 2^x

If binary string is “1000” then we have to perform only 1 operation i.e. Add 2³

If binary string is “101” then we have to perform 2 operations i.e. Add 2² + 2⁰

Example

#include <iostream>
#include <string>
#include <algorithm>
using namespace std;
int getMinOperations(string s){
   reverse(s.begin(), s.end());
   int n = s.length();
   int result[n + 1][2];
   if (s[0] == '0') {
      result[0][0] = 0;
   } else {
      result[0][0] = 1;
   }
   result[0][1] = 1;
   for (int i = 1; i < n; ++i) {
      if (s[i] == '0') {
         result[i][0] = result[i - 1][0];
         result[i][1] = 1 + min(result[i - 1][1],
         result[i - 1][0]);
      } else {
         result[i][1] = result[i - 1][1];
         result[i][0] = 1 + min(result[i - 1][0],
         result[i - 1][1]);
      }
   }
   return result[n - 1][0];
}
int main(){
   string str = "101";
   cout << "Minimum required operations = " << getMinOperations(str) << endl;
   return 0;
}

Output

When you compile and execute above program. It generates following output −

Minimum required operations = 2